An investigation of the robustness in the Travelling Salesman problem routes using special structured matrices
In this study, the robustness of the Travelling Salesman Problem (TSP) routes is investigated by recognising the special combinatorial structures of Kalmanson matrices. A recognition algorithm encompassing three procedures based on combinatorial and linear programming (LP) is developed and executed on several randomly generated instances. These procedures produce three lower bounds which provide guarantees on the optimality of the solutions. Computational experiments show that the proposed LP-based procedure performs efficiently well across all problem dimensions and provides the best lower bounds to the TSP. This is supported by an average deviation of less than 7% between the TSP tour lengths and the lower bounds of the Kalmanson matrices.
Aziz, Azmin Azliza; Mousavi, Seyed Mohsen; Tavana, Madjid; and Niaki, Seyed Taghi Akhavan, "An investigation of the robustness in the Travelling Salesman problem routes using special structured matrices" (2020). Business Systems and Analytics Faculty Work. 61.